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Find the area of the triangle

Source: Cono Sur 2003 #4

November 18, 2015
geometrycono sur

Problem Statement

In an acute triangle ABCABC, the points HH, GG, and MM are located on BCBC in such a way that AHAH, AGAG, and AMAM are the height, angle bisector, and median of the triangle, respectively. It is known that HG=GMHG=GM, AB=10AB=10, and AC=14AC=14. Find the area of triangle ABCABC.
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